Development of Design Method for Supersonic Turbine Aerofoils Near the Tip of Long Blades in Steam Turbines: Part 2 — Configuration Details and Validation

Abstract

Both inflow and outflow velocities near the blade tip become supersonic when the blade length exceeds a threshold limit. The aerofoil near the tip of such a long blade has four features that demand an original supersonic turbine aerofoil design: supersonic flow in the entire field, high reaction, large stagger angle, and large pitch-to-chord ratio. This paper describes design method development for the supersonic turbine aerofoil. First, the aerofoil shape is defined using a curve with continuity in the gradient of the curvature. Second, six loss generation mechanisms are clarified by turbulent flow analysis. Third, an allowable design space between the pitch-to-chord ratio, the stagger angle and the axial-chord-to-pitch ratio is clarified by formulating three geometrical constraints to accelerate supersonic flow smoothly. When there is no solution in the theoretically allowable design space because of the large pitch-to-chord ratio, methods to reduce shock wave losses are proposed. Increasing the outlet metal angle of the pressure surface by around 10 deg from the theoretical outlet flow angle reduces the loss caused by the trailing shock wave. The physical mechanism for this is as follows: the increased outlet metal angle increases the outlet flow passage area so that the overexpansion is suppressed downstream from the flow passage. Fourth, both a cusped leading edge and an upstream pressure surface which has both an angle corresponding to the inflow angle and near-zero curvature can reduce the loss caused by the leading shock wave and satisfy the unique incidence relation. Finally, the aerodynamic performance of the supersonic turbine cascade and the design method are validated by supersonic cascade wind tunnel tests.

One-Dimensional Assessment of Supersonic Inlet Turbines

“…Fig. 7 Turbine leading edge shock wave modelling Senoo and Ono [9] and Dvorák et al [10] proposed the use of wedge type leading edges for transonic steam turbine airfoils. Wedge type leading edges reduce the intensity of the shock waves resulting in significant aerodynamic improvements.…”

“…6) the local upstream Mach number needs to be evaluated. Based on the location of the sonic line, the Mach number passed the leading edge expansion fan is computed using the Prandlt-Meyer function, Eq(9). The turning angle downstream of the sonic line was approximated to the detachment angle (θ).…”

Turbine Cascades of Last Stage Blades for Wide Range of Operating Conditions

“…The proper stator blade design with advanced 3D shaping is highly important because it has significant impact on the relative velocity in the vicinity of the rotating blade. However, the relative Mach numbers exceeding 1 are commonly present in flow field surrounding the rotating blade due to high tangential velocities and even supersonic flow with inlet shock wave can occur, especially in the case of ultra-long full speed (3000 or 3600 RPM) last stage blades [1]. Final mechanical design must fulfill criteria of static strength which determines strict distribution of area for each section along the blade span.…”

Unsteady flow mechanisms in the last stage of a transonic low pressure steam turbine—multistage effects and tip leakage flows

“…However, the design is quite challenging due to the fact that inlet flow conditions close to tip are supersonic in relative frame of reference. This leads to a generation of a bow shock wave upstream of the rotor's leading edge (Senoo, 2012) that, if not given sufficient space to decay, will interact with the upstream stator blade row, causing high flow unsteadiness or even potential boundary layer separation on the stator and increased kinetic energy losses (Senoo and Ono, 2013).…”